Subgroups — C₂×#29503117 #44476641

Order 30324.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#87704	C₂	1	1	yes	maximal, characteristic, complemented
2	#29503117	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₉×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×#87704	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×D₁₃₃	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×D₁₉×C₁₉⋊C₃	—	7	1	no	maximal, Hall
8	C₇×C₁₉²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₁₉×C₁₉⋊C₃	—	14	1	no	—
10	D₁₉×C₁₉⋊C₃	—	7	2	no	—
11	C₂×#11716325	—	19	1	no	maximal
12	C₂×ΓL(1,𝔽₈)⋊D₁₉	—	19	1	no	maximal
13	C₂×C₁₉×D₁₉	—	7	1	no	Hall
14	C₁₉×C₁₉⋊C₃	—	14	1	no	Hall
15	C₂×#87704	D₁₉	1	1	yes	characteristic, complemented
16	C₂×C₁₉×ΓL(1,𝔽₈)	—	19	1	no	—
17	#11716325	—	19	2	no	—
18	ΓL(1,𝔽₈)⋊D₁₉	—	19	2	no	—
19	C₂×C₁₉²	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₁₉×D₁₉	—	7	2	no	—
21	C₂×D₁₃₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
22	C₂×D₇×C₁₉	—	19	1	no	—
23	#87704	C₂×D₁₉	1	1	yes	characteristic, complemented
24	C₁₉×ΓL(1,𝔽₈)	—	19	1	no	—
25	C₁₉²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₇×C₁₉	—	6	3	no	—
27	C₂×C₇×C₁₉	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
28	C₂×C₇×C₁₉	C₃×D₁₉	1	1	yes	characteristic, complemented
29	D₁₃₃	C₂×C₁₉⋊C₃	1	2	yes	complemented
30	D₇×C₁₉	—	19	2	no	—
31	C₂×C₃×D₁₉	—	133	1	no	—
32	C₂²×C₁₉⋊C₃	—	133	1	no	—
33	C₇×C₁₉	—	6	3	no	—
34	C₇×C₁₉	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
35	C₇×C₁₉	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
36	C₂×C₃×C₁₉	—	266	1	no	—
37	C₃×D₁₉	—	133	2	no	—
38	C₂×C₁₉⋊C₃	—	14	1	no	—
39	C₂×C₁₉⋊C₃	—	133	2	no	—
40	C₂×AGL(1,𝔽₇)	—	361	1	no	Hall
41	C₂²×C₁₉	—	133	1	no	—
42	C₂×D₁₉	—	7	1	no	—
43	C₃×C₁₉	—	266	1	no	—
44	C₁₉⋊C₃	—	14	1	no	—
45	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
46	AGL(1,𝔽₇)	—	361	2	no	—
47	C₂×C₁₉	—	6	3	no	—
48	C₂×C₁₉	—	133	2	no	—
49	C₂×C₁₉	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
50	C₂×C₁₉	#11716325	1	1	yes	characteristic, complemented
51	D₁₉	—	7	2	no	—
52	C₂×D₇	—	19	1	no	Hall
53	ΓL(1,𝔽₈)	—	19	1	no	Hall
54	C₁₉	—	6	3	no	—
55	C₁₉	C₂×ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
56	C₁₉	C₂×#11716325	1	1	yes	characteristic, complemented
57	C₂×C₇	D₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented
58	D₇	—	19	2	no	—
59	C₂²×C₃	—	2527	1	no	Hall
60	C₇	C₂×D₁₉×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₃	—	266	1	no	—
62	C₂×C₃	—	2527	2	no	—
63	C₂²	—	133	1	no	Sylow
64	C₃	—	266	1	no	Sylow
65	C₂	—	133	2	no	—
66	C₂	#29503117	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#29503117
commutator, cosocle, hypocenter	C₇×C₁₉²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉²	C₂×C₃
LCS	G ▷ C₇×C₁₉²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#87704	C₂	semidirect
2. #29503117	C₂	direct (N × H)
3. C₂×C₁₉×D₁₃₃	C₃	semidirect
4. C₁₉×#87704	C₂²	semidirect
5. C₁₉×D₁₃₃	C₂×C₃	semidirect
6. C₂×C₇×C₁₉²	C₂×C₃	semidirect
8. C₇×C₁₉²	C₂²×C₃	semidirect
15. C₂×#87704	D₁₉	semidirect
19. C₂×C₁₉²	AGL(1,𝔽₇)	semidirect
21. C₂×D₁₃₃	C₁₉⋊C₃	semidirect
23. #87704	C₂×D₁₉	semidirect
25. C₁₉²	C₂×AGL(1,𝔽₇)	semidirect
27. C₂×C₇×C₁₉	C₂×C₁₉⋊C₃	semidirect
28. C₂×C₇×C₁₉	C₃×D₁₉	semidirect
29. D₁₃₃	C₂×C₁₉⋊C₃	semidirect
34. C₇×C₁₉	C₂²×C₁₉⋊C₃	semidirect
35. C₇×C₁₉	C₂×C₃×D₁₉	semidirect
49. C₂×C₁₉	ΓL(1,𝔽₈)⋊D₁₉	semidirect
50. C₂×C₁₉	#11716325	semidirect
55. C₁₉	C₂×ΓL(1,𝔽₈)⋊D₁₉	semidirect
56. C₁₉	C₂×#11716325	semidirect
57. C₂×C₇	D₁₉×C₁₉⋊C₃	semidirect
60. C₇	C₂×D₁₉×C₁₉⋊C₃	semidirect
66. C₂	#29503117	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×C₁₉×#87704	2
#29503117	2
C₂×C₁₉×D₁₃₃	3
C₂×D₁₉×C₁₉⋊C₃	7
C₂×#11716325	19
C₂×ΓL(1,𝔽₈)⋊D₁₉	19

Subgroups — C2×#29503117 #44476641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#29503117 #44476641