Subgroups — C₂×C₃⋊((C₁₃⋊C₃)⋊D₆₇) #44535768

Order 31356.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃⋊C₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₁₃⋊C₃)⋊D₆₇)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₆₁₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₁₃⋊C₃)⋊D₆₇	—	3	1	no	maximal
5	C₃×C₁₃⋊C₃×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	(C₁₃⋊C₃)⋊D₆₇	—	3	2	no	—
7	D₂₆₁₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃⋊C₃×C₆₇	—	2	1	no	—
9	C₂×C₁₃⋊C₃×C₆₇	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₈₇₁	—	3	1	no	Hall
12	C₃×C₁₃×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₃⋊C₃×C₆₇	—	2	1	no	—
14	C₁₃⋊C₃×C₆₇	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₂₀₁	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic, complemented
17	D₈₇₁	—	3	2	no	—
18	C₂×C₃²×C₆₇	—	13	1	no	—
19	C₃×D₂₀₁	—	13	2	no	—
20	C₁₃×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₂₀₁	—	13	1	no	—
22	C₂×C₃×D₆₇	—	39	1	no	—
23	C₃²×C₆₇	—	13	1	no	Hall
24	C₂×C₃⋊(D₁₃⋊C₃)	—	67	1	no	maximal, Hall
25	C₂×C₃×C₆₇	—	13	1	no	—
26	C₂×C₃×C₆₇	—	26	1	no	—
27	C₂×C₃×C₆₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
28	D₂₀₁	—	13	2	no	—
29	C₃×D₆₇	—	39	2	no	—
30	C₂×D₆₇	—	39	1	no	Hall
31	C₂×C₃×C₁₃⋊C₃	D₆₇	1	1	yes	characteristic, complemented
32	C₃⋊(D₁₃⋊C₃)	—	67	2	no	—
33	C₃×C₆₇	—	13	1	no	—
34	C₃×C₆₇	—	26	1	no	—
35	C₃×C₆₇	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
36	C₂×D₃₉	—	67	1	no	—
37	C₂×D₁₃⋊C₃	—	201	1	no	—
38	C₂×C₆₇	C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
39	D₆₇	—	39	2	no	—
40	C₃×C₁₃⋊C₃	C₂×D₆₇	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₁₃	C₃×D₆₇	1	1	yes	characteristic, complemented
42	D₃₉	—	67	2	no	—
43	C₂×C₁₃⋊C₃	—	2	1	no	—
44	C₂×C₁₃⋊C₃	D₂₀₁	1	1	yes	characteristic, complemented
45	D₁₃⋊C₃	—	201	2	no	—
46	C₆₇	C₂×C₃⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₁₃	—	201	1	no	Hall
48	C₃×C₁₃	C₂×C₃×D₆₇	1	1	yes	characteristic, complemented
49	C₁₃⋊C₃	—	2	1	no	—
50	C₁₃⋊C₃	C₂×D₂₀₁	1	1	yes	characteristic, complemented
51	C₂×C₃×D₃	—	871	1	no	Hall
52	C₂×C₁₃	C₃×D₂₀₁	1	1	yes	characteristic, complemented
53	D₁₃	—	201	2	no	—
54	C₂×C₃²	—	13	1	no	—
55	C₃×D₃	—	871	2	no	—
56	C₁₃	C₂×C₃×D₂₀₁	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	2613	1	no	—
58	C₂×D₃	—	871	1	no	—
59	C₃²	—	13	1	no	Sylow
60	C₂×C₃	—	13	1	no	—
61	C₂×C₃	—	26	1	no	—
62	C₂×C₃	—	2613	2	no	—
63	C₂×C₃	(C₁₃⋊C₃)⋊D₆₇	1	1	yes	characteristic, complemented
64	D₃	—	871	2	no	—
65	C₂²	—	2613	1	no	Sylow
66	C₃	—	13	1	no	—
67	C₃	—	26	1	no	—
68	C₃	C₂×(C₁₃⋊C₃)⋊D₆₇	1	1	yes	characteristic, complemented
69	C₂	—	2613	2	no	—
70	C₂	C₃⋊((C₁₃⋊C₃)⋊D₆₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₁₃⋊C₃)⋊D₆₇)
commutator, cosocle, hypocenter	C₃×C₁₃×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃⋊C₃×C₆₇	C₂	semidirect
2. C₃⋊((C₁₃⋊C₃)⋊D₆₇)	C₂	direct (N × H)
3. C₂×D₂₆₁₃	C₃	semidirect
5. C₃×C₁₃⋊C₃×C₆₇	C₂²	semidirect
7. D₂₆₁₃	C₂×C₃	semidirect
9. C₂×C₁₃⋊C₃×C₆₇	D₃	semidirect
10. C₂×C₃×C₁₃×C₆₇	C₂×C₃	semidirect
12. C₃×C₁₃×C₆₇	C₂²×C₃	semidirect
14. C₁₃⋊C₃×C₆₇	C₂×D₃	semidirect
16. C₂×C₁₃×C₆₇	C₃×D₃	semidirect
20. C₁₃×C₆₇	C₂×C₃×D₃	semidirect
27. C₂×C₃×C₆₇	D₁₃⋊C₃	semidirect
31. C₂×C₃×C₁₃⋊C₃	D₆₇	semidirect
35. C₃×C₆₇	C₂×D₁₃⋊C₃	semidirect
38. C₂×C₆₇	C₃⋊(D₁₃⋊C₃)	semidirect
40. C₃×C₁₃⋊C₃	C₂×D₆₇	semidirect
41. C₂×C₃×C₁₃	C₃×D₆₇	semidirect
44. C₂×C₁₃⋊C₃	D₂₀₁	semidirect
46. C₆₇	C₂×C₃⋊(D₁₃⋊C₃)	semidirect
48. C₃×C₁₃	C₂×C₃×D₆₇	semidirect
50. C₁₃⋊C₃	C₂×D₂₀₁	semidirect
52. C₂×C₁₃	C₃×D₂₀₁	semidirect
56. C₁₃	C₂×C₃×D₂₀₁	semidirect
63. C₂×C₃	(C₁₃⋊C₃)⋊D₆₇	semidirect
68. C₃	C₂×(C₁₃⋊C₃)⋊D₆₇	semidirect
70. C₂	C₃⋊((C₁₃⋊C₃)⋊D₆₇)	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×C₃×C₁₃⋊C₃×C₆₇	2
C₃⋊((C₁₃⋊C₃)⋊D₆₇)	2
C₂×D₂₆₁₃	3
C₂×(C₁₃⋊C₃)⋊D₆₇	3
C₂×C₃×D₂₀₁	13
C₂×C₃⋊(D₁₃⋊C₃)	67

Subgroups — C2×C3⋊((C13⋊C3)⋊D67) #44535768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊((C₁₃⋊C₃)⋊D₆₇) #44535768