Subgroups — C₃×Dic₂₂₃₅ #41001256

Order 26820.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₂₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×Dic₇₄₅	—	3	1	no	maximal
4	C₃²×C₅×C₁₄₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₄₄₇	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅×C₁₄₉	—	2	1	no	—
7	C₂×C₃×C₅×C₁₄₉	D₃	1	1	yes	characteristic
8	C₂×C₃×C₅×C₁₄₉	C₂×C₃	1	1	yes	characteristic
9	Dic₇₄₅	—	3	1	no	Hall
10	C₂×C₃²×C₁₄₉	D₅	1	1	yes	characteristic
11	C₃×C₅×C₁₄₉	—	2	1	no	—
12	C₃×C₅×C₁₄₉	Dic₃	1	1	yes	characteristic, complemented
13	C₃×C₅×C₁₄₉	C₃×C₄	1	1	yes	characteristic, complemented
14	Dic₄₄₇	—	5	1	no	—
15	C₃×Dic₁₄₉	—	15	1	no	—
16	C₂×C₅×C₁₄₉	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₁₄₉	Dic₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₄₉	—	2	1	no	—
19	C₂×C₃×C₁₄₉	C₃×D₅	1	1	yes	characteristic
20	C₂×C₃×C₁₄₉	D₁₅	1	1	yes	characteristic
21	C₅×C₁₄₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
22	Dic₁₄₉	—	15	1	no	Hall
23	C₃×C₁₄₉	—	2	1	no	—
24	C₃×C₁₄₉	C₃×Dic₅	1	1	yes	characteristic, complemented
25	C₃×C₁₄₉	Dic₁₅	1	1	yes	characteristic, complemented
26	C₂×C₁₄₉	C₃×D₁₅	1	1	yes	characteristic
27	C₃×Dic₁₅	—	149	1	no	maximal, Hall
28	C₁₄₉	C₃×Dic₁₅	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²×C₅	D₁₄₉	1	1	yes	characteristic
30	Dic₁₅	—	149	1	no	—
31	C₃×Dic₅	—	447	1	no	—
32	C₃²×C₅	Dic₁₄₉	1	1	yes	characteristic, complemented, Hall
33	C₃×Dic₃	—	745	1	no	Hall
34	C₂×C₃×C₅	—	2	1	no	—
35	C₂×C₃×C₅	C₃×D₁₄₉	1	1	yes	characteristic
36	C₂×C₃×C₅	D₄₄₇	1	1	yes	characteristic
37	Dic₅	—	447	1	no	Hall
38	C₂×C₃²	D₇₄₅	1	1	yes	characteristic
39	C₃×C₅	—	2	1	no	—
40	C₃×C₅	C₃×Dic₁₄₉	1	1	yes	characteristic, complemented
41	C₃×C₅	Dic₄₄₇	1	1	yes	characteristic, complemented
42	C₃×C₄	—	2235	1	no	—
43	Dic₃	—	745	1	no	—
44	C₂×C₅	C₃×D₄₄₇	1	1	yes	characteristic
45	C₃²	Dic₇₄₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	C₃×D₇₄₅	1	1	yes	characteristic
48	C₂×C₃	D₂₂₃₅	1	1	yes	characteristic
49	C₅	C₃×Dic₄₄₇	1	1	yes	characteristic, complemented, Sylow
50	C₄	—	2235	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×Dic₇₄₅	1	1	yes	characteristic, complemented
53	C₃	Dic₂₂₃₅	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₂₂₃₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₂₃₅
commutator, hypocenter	C₃×C₅×C₁₄₉	C₃×C₄
Frattini	C₂	C₃×D₂₂₃₅
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₄₉	C₂
cosocle	C₂×C₃×C₅×C₁₄₉	C₂×C₃
LCS	G ▷ C₃×C₅×C₁₄₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₂₂₃₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₄₉	C₄	semidirect
12. C₃×C₅×C₁₄₉	Dic₃	semidirect
13. C₃×C₅×C₁₄₉	C₃×C₄	semidirect
17. C₃²×C₁₄₉	Dic₅	semidirect
21. C₅×C₁₄₉	C₃×Dic₃	semidirect
24. C₃×C₁₄₉	C₃×Dic₅	semidirect
25. C₃×C₁₄₉	Dic₁₅	semidirect
28. C₁₄₉	C₃×Dic₁₅	semidirect
32. C₃²×C₅	Dic₁₄₉	semidirect
40. C₃×C₅	C₃×Dic₁₄₉	semidirect
41. C₃×C₅	Dic₄₄₇	semidirect
45. C₃²	Dic₇₄₅	semidirect
49. C₅	C₃×Dic₄₄₇	semidirect
52. C₃	C₃×Dic₇₄₅	semidirect
53. C₃	Dic₂₂₃₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅×C₁₄₉	2
Dic₂₂₃₅	3
C₃×Dic₇₄₅	3
C₃×Dic₄₄₇	5
C₃×Dic₁₅	149

Subgroups — C3×Dic2235 #41001256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₂₂₃₅ #41001256