Subgroups — C₂×#29503114 #44476643

Order 30324.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21439062	C₂	1	1	yes	maximal, characteristic, complemented
2	#29503114	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₇×C₁₉²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#21439062	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₇×C₁₉²	C₂×C₃	1	2	yes	complemented
6	C₂×C₇×C₁₉²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×#11762245	—	7	1	no	maximal, Hall
8	C₇×C₁₉²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×#11762245	—	7	2	no	—
10	C₂×#11762245	—	7	1	no	—
11	C₂×#11716325	—	19	20	no	maximal
12	C₂²×C₁₉²	—	7	1	no	Hall
13	#11762245	—	7	1	no	Hall
14	C₂×#87704	—	19	20	no	—
15	#11716325	—	19	40	no	—
16	C₂×C₁₉²	—	7	2	no	—
17	C₂×C₁₉²	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
18	C₂×D₇×C₁₉	C₁₉⋊C₃	1	20	yes	complemented
19	#87704	—	19	20	no	—
20	C₁₉²	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₇×C₁₉	C₂×C₁₉⋊C₃	1	20	yes	complemented
22	D₇×C₁₉	C₂×C₁₉⋊C₃	1	40	yes	complemented
23	C₂²×C₁₉⋊C₃	—	133	20	no	—
24	C₇×C₁₉	C₂²×C₁₉⋊C₃	1	20	yes	complemented
25	C₂×C₁₉⋊C₃	—	133	40	no	—
26	C₂×C₁₉⋊C₃	—	133	20	no	—
27	C₂×AGL(1,𝔽₇)	—	361	1	no	Hall
28	C₂²×C₁₉	—	7	20	no	—
29	C₁₉⋊C₃	—	133	20	no	—
30	C₂×ΓL(1,𝔽₈)	—	361	1	no	—
31	AGL(1,𝔽₇)	—	361	2	no	—
32	C₂×C₁₉	—	7	40	no	—
33	C₂×C₁₉	#11716325	1	20	yes	complemented
34	C₂×D₇	#11762245	1	1	yes	characteristic, complemented, Hall
35	ΓL(1,𝔽₈)	—	361	1	no	Hall
36	C₁₉	C₂×#11716325	1	20	yes	complemented
37	C₂×C₇	C₂×#11762245	1	1	yes	characteristic, complemented
38	D₇	C₂×#11762245	1	2	yes	complemented
39	C₂²×C₃	—	2527	1	no	Hall
40	C₇	C₂²×#11762245	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	2527	2	no	—
42	C₂×C₃	—	2527	1	no	—
43	C₂²	—	7	1	no	Sylow
44	C₃	—	2527	1	no	Sylow
45	C₂	—	7	2	no	—
46	C₂	#29503114	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#29503114
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×#21439062	C₂	semidirect
2. #29503114	C₂	direct (N × H)
3. C₂×D₇×C₁₉²	C₃	semidirect
4. #21439062	C₂²	semidirect
5. D₇×C₁₉²	C₂×C₃	semidirect
6. C₂×C₇×C₁₉²	C₂×C₃	semidirect
8. C₇×C₁₉²	C₂²×C₃	semidirect
17. C₂×C₁₉²	AGL(1,𝔽₇)	semidirect
18. C₂×D₇×C₁₉	C₁₉⋊C₃	semidirect
20. C₁₉²	C₂×AGL(1,𝔽₇)	semidirect
21. C₂×C₇×C₁₉	C₂×C₁₉⋊C₃	semidirect
22. D₇×C₁₉	C₂×C₁₉⋊C₃	semidirect
24. C₇×C₁₉	C₂²×C₁₉⋊C₃	semidirect
33. C₂×C₁₉	#11716325	semidirect
34. C₂×D₇	#11762245	semidirect
36. C₁₉	C₂×#11716325	semidirect
37. C₂×C₇	C₂×#11762245	semidirect
38. D₇	C₂×#11762245	semidirect
40. C₇	C₂²×#11762245	semidirect
46. C₂	#29503114	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×#21439062	2
#29503114	2
C₂×D₇×C₁₉²	3
C₂²×#11762245	7
C₂×#11716325	19

Subgroups — C2×#29503114 #44476643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#29503114 #44476643