Finite Group Databasebeta

← #14284017

Subgroups — #14284017

Order 1920.

452 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 102 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#11752498C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic
3#11747003C211yesmaximal, characteristic
4#11746286C211yesmaximal, characteristic, complemented
5C5×#4465C211yesmaximal, characteristic, complemented
6#11745851C211yesmaximal, characteristic, complemented
7#11745850C211yesmaximal, characteristic, complemented
8#10599155—31nomaximal, Hall
9#91759C2211yescharacteristic
10C5×#870C2211yescharacteristic
11C2×C3×#676—21no—
12C3×C42×D5C2211yescharacteristic
13#91468C411yescharacteristic
14#91468C411yescharacteristic
15#91358C411yescharacteristic
16#91358C411yescharacteristic
17#91349—21no—
18#91349—21no—
19#91323—21no—
20#91323—21no—
21C2×#6649—21no—
22C3×C5×#97C2211yescharacteristic
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic
27Dic5×C3⋊C8—21no—
28#69862—51nomaximal, Hall
29#66022—31no—
30#64996—31no—
31#64996D311yescharacteristic
32C5×#330—31no—
33#64763—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C4×D5C2×C411yescharacteristic
37C2×C3×C4×D5D411yescharacteristic
38C2×C3×C4×D5D411yescharacteristic
39C2×#1204—21no—
40C2×#1204—21no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15C2×C411yescharacteristic
44C4⋊Dic15C2×C411yescharacteristic
45#6712—21no—
46#6712—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3C2×C411yescharacteristic
49C5×C4⋊Dic3C2×C411yescharacteristic
50C5×Dic3⋊C4—21no—
51C5×Dic3⋊C4—21no—
52C2×C5×C3⋊C8—21no—
53C3×C4×Dic5C2×C411yescharacteristic
54C3×C4×Dic5D411yescharacteristic
55C3×C4×Dic5D411yescharacteristic
56C2×C3×#168—21no—
57C3×#676—24no—
58#6668—21no—
59#6668—21no—
60#6665—21no—
61#6665—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5—21no—
64#6649—24no—
65#5470—51no—
66C3×C4×M16—51no—
67C4×#208—51no—
68#4465—51no—
69#4465—51no—
70#4465—51no—
71#4465D511yescharacteristic, complemented
72C5×#125—31no—
73C2×#676—21no—
74C2×#676—61no—
75#4042—61no—
76#4042—61no—
77#4038—31no—
78#4038—31no—
79#4034—31no—
80#4034—31no—
81#4033—61no—
82#4033—61no—
83C42×D5C2×D311yescharacteristic
84#4016—31no—
85C5×#97—31no—
86C5×#97C2×D311yescharacteristic
87C8×Dic5—21no—
88C8×Dic5—61no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1526—151noSylow
92C22×C3×D5C22⋊C411yescharacteristic
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C2×C3×Dic5C22⋊C411yescharacteristic
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C22⋊C411yescharacteristic
103C3×C4×D5—22no—
104C3×C4×D5—22no—
105C3×C4×D5—22no—
106#1204—42no—
107#1204—42no—
108C3×C5×C8—22no—
109C3⋊#168—22no—
110C3×#168—22no—
111C5×C3⋊C8—22no—
112C2×C3×M16—101no—
113C2×C3×C42—51no—
114#926—51no—
115#926—51no—
116#924—101no—
117#924—101no—
118C2×#208—101no—
119#870—51no—
120#870C2×D511yescharacteristic
121#869—51no—
122#869—51no—
123C4×Dic6—101no—
124C4×Dic6—101no—
125C3×#97—51no—
126C3×#97C2×D511yescharacteristic
127C3×C4×C8—101no—
128#803—51no—
129#803C2×D511yescharacteristic
130C4×C3⋊C8—101no—
131C2×C4×D5C4×D311yescharacteristic
132C2×C4×D5D1211yescharacteristic
133C2×C4×D5#6711yescharacteristic
134C2×Dic10—61no—
135C2×Dic10—61no—
136C2×C5×C8—21no—
137C2×C5×C8—61no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#685—61no—
144#685—61no—
145C4⋊Dic5—31no—
146C4⋊Dic5—31no—
147#683—61no—
148#683—61no—
149#683—61no—
150#683—61no—
151C4×Dic5—61no—
152C4×Dic5—61no—
153C4×Dic5C4×D311yescharacteristic
154C4×Dic5D1211yescharacteristic
155C4×Dic5#6711yescharacteristic
156C2×#168—21no—
157C2×#168—61no—
158#676—24no—
159#676—64no—
160#533—151no—
161C4×M16—51no—
162C4×M16—151no—
163#330—31no—
164#330—151no—
165#330—151no—
166#330—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174Dic15—41no—
175Dic15—41no—
176C3×Dic5#10112yes—
177C3×Dic5#10412yes—
178C3×Dic5#10412yes—
179C5×Dic3—41no—
180C5×Dic3—41no—
181C22×C3×C4—51no—
182C22×C3×C4—51no—
183C22×C3×C4—51no—
184C2×Dic6—101no—
185C2×Dic6—101no—
186C3×M16—104no—
187C2×C3×C8—21no—
188C2×C3×C8—101no—
189C3×C42—51no—
190C3×C42—51no—
191C3×C42—51no—
192C3×C42C22×D511yescharacteristic
193#217—101no—
194#217—101no—
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197C4⋊Dic3—101no—
198C4⋊Dic3—101no—
199C4⋊Dic3C4×D511yescharacteristic
200C4⋊Dic3C4×D511yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205C4×Dic3—101no—
206C4×Dic3—101no—
207#208—104no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—101no—
210C22×D5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5—61no—
212C2×C4×C5—61no—
213C2×C4×C5C2×C4×D311yescharacteristic
214C2×C4×C5C2×D1211yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×Dic5—61no—
217C2×Dic5—61no—
218C2×Dic5(C2×D3)⋊C411yescharacteristic
219C2×Dic5(C2×D3)⋊C411yescharacteristic
220C2×Dic5(C2×D3)⋊C411yescharacteristic
221C4×D5—22no—
222C4×D5—22no—
223C4×D5—22no—
224Dic10—122no—
225Dic10—122no—
226C5×C8—22no—
227C5×C8—62no—
228#168—22no—
229#168—62no—
230C2×M16—101no—
231C2×M16—301no—
232C4⋊Q8—151no—
233C4⋊Q8—151no—
234#125—31no—
235#125—151no—
236C22⋊Q8—301no—
237C22⋊Q8—301no—
238C4×Q8—301no—
239C4×Q8—301no—
240#117—151no—
241#117—151no—
242C2×C42—51no—
243#97—31no—
244#97—51no—
245#97—151no—
246#97D3×D511yescharacteristic
247C4×C8—101no—
248C4×C8—301no—
249C2×C3×C5C2×#10111yescharacteristic
250C2×C3×C5C2×#10411yescharacteristic
251C2×C3×C5C2×#10411yescharacteristic
252C3×D5—41no—
253C23×C3—51no—
254C2×C3×C4—51no—
255C2×C3×C4—51no—
256C2×C3×C4—51no—
257C2×C3×C4—102no—
258C2×C3×C4—102no—
259C2×C3×C4—102no—
260C2×C3×C4C2×C4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267Dic6—202no—
268Dic6—202no—
269C3×C8—22no—
270C3×C8—102no—
271C3⋊C8—22no—
272C3⋊C8—102no—
273C22×C5C2×(C2×D3)⋊C411yescharacteristic
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—21no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—21no—
280C4×C5—121no—
281C4×C5—121no—
282Dic5—121no—
283Dic5—121no—
284Dic5#80512yes—
285Dic5#82412yes—
286Dic5#82512yes—
287C2×Q8—301no—
288C2×Q8—301no—
289C22×C4—51no—
290C22×C4—51no—
291C22×C4—51no—
292M16—104no—
293M16—304no—
294C2×C8—21no—
295C2×C8—61no—
296C2×C8—101no—
297C2×C8—301no—
298C4⋊C4—31no—
299C4⋊C4—31no—
300C4⋊C4—61no—
301C4⋊C4—61no—
302C4⋊C4—151no—
303C4⋊C4—151no—
304C4⋊C4—301no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4—301no—
308C22⋊C4—301no—
309C22⋊C4—301no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42—301no—
314C42—301no—
315C42C2×D3×D511yescharacteristic
316C3×C5#152611yescharacteristic, complemented, Hall
317C22×C3—101no—
318C22×C3—101no—
319C22×C3—101no—
320C22×C3D5×C22⋊C411yescharacteristic
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—52no—
325C3×C4—52no—
326C3×C4—52no—
327Dic3—41no—
328Dic3—41no—
329Dic3—201no—
330Dic3—201no—
331C2×C5C2×#80511yescharacteristic
332C2×C5C2×#82411yescharacteristic
333C2×C5C2×#82511yescharacteristic
334D5—41no—
335C23—51no—
336Q8—602no—
337Q8—602no—
338C2×C4—51no—
339C2×C4—51no—
340C2×C4—51no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—102no—
344C2×C4—102no—
345C2×C4—102no—
346C2×C4—301no—
347C2×C4—301no—
348C2×C4C4×D3×D511yescharacteristic
349C2×C4D5×D1211yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C8—22no—
352C8—62no—
353C8—102no—
354C8—302no—
355C2×C3—201no—
356C2×C3D5×#10111yescharacteristic
357C2×C3D5×#10411yescharacteristic
358C2×C3D5×#10411yescharacteristic
359C5#6986211yescharacteristic, complemented, Sylow
360C22—101no—
361C22—101no—
362C22—101no—
363C22D5×(C2×D3)⋊C411yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—52no—
368C4—52no—
369C4—52no—
370C4—121no—
371C4—121no—
372C4—601no—
373C4—601no—
374C3#1059915511yescharacteristic, complemented, Sylow
375C2—201no—
376C2D5×#80511yescharacteristic
377C2D5×#82411yescharacteristic
378C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C22⋊C4
cosocleC3×C42×C5C23
hypercenter#97D3×D5
hypocenterC3×C5#1526
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. #11746286C2semidirect
5. C5×#4465C2semidirect
6. #11745851C2semidirect
7. #11745850C2semidirect
71. #4465D5semidirect
316. C3×C5#1526semidirect
359. C5#69862semidirect
374. C3#10599155semidirect

Maximal subgroups

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

subgroupindex
#117524982
C3×#649962
#117470032
#117462862
C5×#44652
#117458512
#117458502
#105991553
#698625